This is an intermediate course on functional analysis. Building on MAT4400, you will learn about
- advanced topics in measure theory: product measures, relation to duality, modes of convergence, etc.
- fundamental topics in Banach spaces: bounded linear forms, bounded linear maps, etc.
These are essential for mathematical foundation of probabilistic concepts such as conditional expectation and Martingale convergence. Banach space part is important for understanding various operations and conditions on function spaces, and will be further developed in MAT4450.
The content will be (loosely) based on
- Bruce Driver "Analysis tools with examples" Chapters 18, 20, 24, 25, 28, 30
In any case, I will make a self contained note, uploaded to the course website along the lectures.